Measurement of the Stefan-Boltzmann constant

[MatinSAR]

Homework Statement

Report the measurement result of the experiment.

Relevant Equations

None.

I've written it as :

The mentor indicated that this is incorrect. How can I write it correctly?
My try: $$ \sigma = 1.07 \times 10^{-8}W.m^{-2}.k^{-4} \pm 0.0243 \times 10^{-8} W.m^{-2}.k^{-4} $$

 

[haruspex]

Homework Statement: Report the measurement result of the experiment.
Relevant Equations: None.

I've written it as :
View attachment 347777
The mentor indicated that this is incorrect. How can I write it correctly?
My try: $$ \sigma = 1.07 \times 10^{-8}W.m^{-2}.k^{-4} \pm 0.0243 \times 10^{-8} W.m^{-2}.k^{-4} $$

First, I assume you mean the Stefan-Boltzmann constant.
The value is somewhat off. https://www.techtarget.com/whatis/definition/Stefan-Boltzmann-constant gives five times as much.
You have more decimal places in the error range than in the central value. But I am not sure whether you should round it to 0.02 or 0.03.
Also, in the typed form above, you have k instead of K.

 

[MatinSAR]

First, I assume you mean the Stefan-Boltzmann constant.

Yes, I edited that.

The value is somewhat off.

We did not use high-precision instruments. The main goal was to learn more about blackbody radiation, rather than focusing on obtaining precise measurements of the constant.

You have more decimal places in the error range than in the central value. But I am not sure whether you should round it to 0.02 or 0.03.
Also, in the typed form above, you have k instead of K.

Thank you for your help. $$\sigma = 1.07 \times 10^{-8}W.m^{-2}.K^{-4} \pm 0.02 \times 10^{-8} W.m^{-2}.K^{-4} $$

 

[Steve4Physics]

In addition to what @haruspex said...

If using the form $a \pm b$, use the same number of decimal places for $a$ and $b$ The units are written only once.

For example, a distance in metres:
$11.0032 \pm 0.0008$ m.

For example, a time in seconds using standard form:
$(9.20 \pm 0.15) \times 10^{-6}$ s
(some people don’t use the brackets).

There is another common method. The above examples can be written more succinctly as
$11.0032(8)$ m and
$9.20(15) \times 10^{-6}$ s.

Edit -typo

 

[MatinSAR]

In addition to what @haruspex said...

If using the form $a \pm b$, use the same number of decimal places for $a$ and $b$ The units are written only once.

For example, a distance in metres:
$11.0032 \pm 0.0008$ m.

For example, a time in seconds using standard form:
$(9.20 \pm 0.15) \times 10^{-6}$ s
(some people don’t use the brackets).

There is another common method. The above examples can be written more succinctly as
$11.0032(8)$ m and
$9.20(15) \times 10^{-6}$ s.

Edit -typo

I get it. Thank you for your time.

 

[vela]

The units should also be typeset in non-italics, and there should be a space between the number and the units.

 

[MatinSAR]

The units should also be typeset in non-italics, and there should be a space between the number and the units.

I will keep this in mind for the future. Thank you.